A Drake Equation for Linguistic Diversity

Peter Edwin Hook
pehook@umich.edu

The Drake
Equation is familiar to students of exobiology and SETI (Search for Extraterrestrial
Intelligence) as a means of stimulating thinking about the number N of
communicating civilizations that might be expected to exist in a given
volume of space. Drake conceived of N as a function of seven variables
each one of which is subject to change with improvements in our knowledge
of cosmology, stellar evolution, biology, and the development of
civilization. As there has not been much non-fictional work recently in
the area of "exolinguistics", it seemed
that it would be an interesting problem to consider what might be some of
the variables that, both at a given time and across time, contribute to
determining the number of languages that are spoken on a planet which is,
like ours, isolated.

For this conceptual exploration I am assuming normal physics and
languages that operate through the oral-aural or manual-visual channels
familiar to us here. I also assume that the emergence of language
confers such enormous and immediate benefits on its "inventors" that there
is no opportunity for it to become hard-wired: Wherever it emerges
language is socially transmitted and hence unstable.

1. P = population. The number of languages cannot be larger than
the total number of individuals capable of speech divided by the number
in a stable band which is about twenty-five. While developing worlds soon
cease to be hospitable to the existence of small self-sufficient groups,
the figure twenty-five applied to an assumed total hunter-gatherer
population of twenty-five million individuals implies a maximum number of
coexistent languages of one million. This large number is a theoretical
limit which is subject to reduction by other terms in the equation.

2. R* = rate of (irreversible) sound or gesture change (ie,
phonological merger). If this factor creates barriers to mutual
comprehension at a rate slower than the rate at which groups split into
separate bands, then sets of bands will share languages even if they do
not interact. For instance, if the cumulative effect of sound change is
sufficient to prevent communication after 500 years and if the average
band splits in two every 100 years, then N would have to be divided by 32.

3. T = topological scale-invariance. The basic idea is that
certain geographies of habitat favor isolation of groups while others
promote their interaction. At early epochs a high degree of
inhomogeneity in the configuration and connectivity of planetary terrain
would favor linguistic diversity. However, by also allowing the
accumulation of technological and economic inequalities large-scale
topological inhomogeneity may lead ultimately to sudden cultural
expansions and colonial situations that reduce linguistic diversity.

4. I = intensity of interaction with foreigners. The more
frequently individuals speaking different languages must interact, the
smaller (over time) the number of languages they use becomes. In general,
the more specialized and diverse an epoch's range of activities, the fewer
the individuals involved in each of them and the more likely it is for
them to need to communicate with foreigners.

5. M = multivalency. The more massive that communicative
leverage becomes the fewer the languages that can support it. Economies of
scale in evolving technologies of communication operate to favor audiences
that are as large as possible, that is, audiences that have a language in
common.

6. Tr = translation cost. If translation cost comes down over
time this variable may counter and even cancel the effects of the two
preceding. A world in which cheap and
immediate translation is easily available is one in which a larger
number of languages can coexist. (For a related discussion see "The
Rosetta Hack" in Scientific American, Nov. 1996.)

7. SLA = second language acquisition cost. This is the flip-side
of translation cost: The more cheaply accurate translations (or
interpretation) can be made the less need for individuals to incur the
costs of learning second and third languages. The largest component of
SLA is the opportunity cost (= time lost) to the learner. Opportunity
costs continue to rise as civilizations evolve.

Upshot. The value of N is highly dependent on a world's level of
socio-economic and technological development. On worlds moving rapidly
towards economic and technological homogeneity, all the parameters in this
equation (except for Tr) should evolve in ways that favor a minimal value
for N.

Question: Are there any economic, scinetific, or technological
benefits in maintaining a value larger than 1 for N? A November 1996
article in Science (274:1479-80) by Van Alstyne and Brynjolfsson
suggests that the ease of communication fostered by developments like
the Internet may balkanize
the scientific community by making it too easy for scientists to limit
their interactions to small sets of like-minded colleagues and to ignore
discourse in other fields. Assuming that a progressive reduction in the
number of languages can be compared to the removal of geographical
barriers to communication that is being effected by the Internet, we might
expect a similar disadvantage to result. However, Van Alstyne and
Brynjolfsson's views on the long-term effects of the Internet are
hotly contested.